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AMERICAN ARCHAEOLOGY AND ETHNOLOGY 

Vol. 12, No. 5, pp. 195-218, plates 1-5 October 1 1, 1916 



ON PLOTTING THE INFLECTIONS OF 
THE VOICE 



BY 

CORNELIUS B. BRADLEY 



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UNIVERSITY OF CALIFORNIA PUBLICATIONS 

IN 

AMERICAN ARCHAEOLOGY AND ETHNOLOGY 

Vol. 12, No. 5, pp. 195-218, plates 1-5 October 11, 1916 



ON PLOTTING THE INFLECTIONS OF THE 

VOICE 

BY 

COENELIUS B. BEADLEY 



PREFATORY NOTE 
When first undertaken, the study which forms the subject of this 
paper was no more than a mere incident in the attempt to clear up 
the confusion and uncertainty which till then had beset a certain 
question of phonetics, namely, the precise nature of the tonal inflec- 
tions or modulations which, in languages of the Chinese type, are 
essential features of every spoken word. The conclusions reached 
through scientific analysis and measurement of wave-lengths could 
not be made convincing and conclusive without the help of a thoroughly 
accurate and trustworthy scheme for representing them visually. The 
time and the effort actually spent in perfecting such a scheme, which 
is, of course, a mere instrument, may seem altogether disproportionate 
to the end in view. But the perfect instrument was in this case 
absolutely necessary to the attainment of the end; and a scientific 
quest is not to be lightly abandoned because the tools for it are not 
ready to hand. 

The scheme finally worked out is one which enables the student 
to translate accurately to the eye the physical facts which the ear 
reads as figure or movement within the field of pitch. It was shaped 
for a definite and single use. But a perfected instrument often finds 
much wider use than that for which it was shaped at first. So I 
have been encouraged to make it known, in order that it may be within 
the reach of all who may have occasion to use it. Already it is likely 
to be tried in the attempt to improve and enrich the speech of deaf- 
mutes, which is pitifully lacking in the element of tone, chiefly because 
of the difficulty of conveying to the sufferers any intelligible ideas 
or suggestions concerning modulation of the voice. 



196 



University of California Publications in Am. Arch, and Ethn. [Vol. 12 



To my colleagues of the Department of Anthropology of the Uni- 
versity of California — Drs. Pliny E. G-oddard, A. L. Kroeber. and 
T. T. Waterman — I am greatly indebted: to the first for the initial 
impulse received as I watched his work in recording Indian speech; 
to all of them in succession for generous and untiring assistance 
in securing the numerous records of the voice which formed 
the material of my studies; and especially to Dr. AYaterman for the 
unfailing interest and enthusiasm with which he has followed my 
work — a stimulus without which I doubt whether this particular 
phase of that work would ever have been brought to completion. 

Some years ago I chanced to call one day at the Anthropological 
Laboratory of the University of California, and found my colleagues 
there deeply engaged in study of instrumental records of Indian 
speech. They were kind enough to show me the Rousselot apparatus, 
and to illustrate its working by taking a few records of my own 
utterance of Siamese speech, which is my other vernacular. 

My friends were interested at once in the peculiar sharp explosion 
(without aspiration) of my oriental p, t, and k, as shown in the record, 
contrasting strongly with the windy utterance given these consonants 
in our speech. But as I followed the delicate sinuous tracing of the 
vowels, it suddenly flashed upon me that each of those tiny waves 
was the record of the air-pulse from one vibration of the vocal chords ; 
that its length was the direct measure of the time elapsed during 
that vibration, and consequently of the pitch of the voice at that 
particular instant. I knew then that I had within my grasp the 
definite settlement of the age-long dispute over the "tones" of 
oriental speech. The pitch of every portion of the vowel-note could 
be absolutely determined by physical measurement of those waves, 
and the whole movement or inflection of voice could thus be accurately 
plotted on paper. We then should have irrefragable demonstration 
of the precise nature of these "tones," instead of irreconcilable 
discrepancies between the sense-impressions of untrained observers on 
the one hand, and. on the other, the idle fancies embodied in the 
native tradition and nomenclature. So. with Dr. Goddard's kind help, 
I presently secured a series of records of each of the five "tones" 
of the Siamese language. 1 

1 A number of these records are shown in Plate 1. Those used in this 
study were all taken at the highest speed of the apparatus, so as to facilitate 
measurement by giving the greatest possible length to the waves in the tracing. 
The working of the machine and the method of securing the records may be 



1916] Bradley: On Plotting the Inflections of the Voice 197 



Finding myself at that time too busy with my regular duties to 
carry this investigation further. I laid the records aside; but later, 
when I went abroad for a year of study in the Orient. I took the 
records with me. There, in the intervals of a larger quest, I found 
time to work out the results. 

First came the measurements. The records of the various "tones" 
showed anywhere from 50 to 150 separate waves. At first an attempt 
was made to measure these one by one with a micrometer. After full 
trial, however, this scheme was abandoned, not so much because of 
the time and effort it involved, as because time and effort so spent 
were largely wasted. The exactness attainable by the micrometer was 
rendered of no avail because of the impossibility of determining with 
equal exactness the points between which the measurements were 
to be taken. For, while the larger phases of the waves were obvious 
enough, the determination of the exact point which should mark crest 
or hollow was as nearly impossible as it would be in the case of a 
sea-wave. So. to reduce to a minimum the inevitable errors of judg- 
ment, recourse was had to measuring the waves in small groups 
together, and reading the scale with a vernier-glass to the nearest 
hundredth of an inch. 2 Of the measurements so made, the smallest 



briefly described as follows: The various air-pulses originating in the vocal 
apparatus are transmitted to a sensitive tympanum or drum, which in turn 
actuates a recording pen. Every separate impulse received by the tympanum 
gives the pen a slight thrust to one side, from which the elasticity of the 
tympanum promptly brings it back. The recording point lightly touches the 
surface of a sheet of smoked paper wrapped about a revolving brass cylinder 
driven by clock-work at a uniform rate of speed. So long as the tympanum 
is undisturbed by air-pulses, the point traces a perfectly straight white line 
around the cylinder. If one speaks into the receiver, each consonant breaks 
the smooth straight line for an instant into sudden and angular commotion, 
while the vowel-tones ruffle it into a series of regular waves which are often 
embroidered or fringed by delicate ripples or cusps caused by the overtones 
of the voice or by the resonance of the chambers of the vocal apparatus. 
These features of the vowel-tracings may be readily seen in the examples 
shown in Plate 1. Since the paper moves at a uniform rate under the record- 
ing point, the measurement of any one of the primary waves in the record 
will give its pitch relatively to the others; for pitch is determined by frequency 
of vibration. 

For a fuller description of the apparatus and of its workings, see P. E. 
Goddard, ' ' A Graphic Method of Eecording Songs, ' ' in Boas Memorial Volume, 
p. 137. 

2 In the first experiments the waves were measured in groups of three. 
Later the number was increased to five, with no appreciable loss in accuracy. 
For the inflections of speech, unlike those of music, are true glides, with no 
abrupt steps or breaks which might be concealed or obscured under these 
averages. And in any case the thing sought is the general figure or pattern 
of the voice-inflection rather than its minute detail, which varies greatly with 
every utterance. 

These measurements were recorded just as they were taken, without reduc- 
ing them to the average of each group. Eeduction was unnecessary, since 
in either case they represent ratios, and not concrete quantities. Furthermore, 
they are liable to reduction later to adjust them to the amended scheme yet 
to be described, and that single operation suffices for all. 



198 University of California Publications in Am. Arch, and Ethn. [Vol. 12 

in the whole series was 18 hundredths of an inch, and the largest 
64 hundredths, showing a compass of a little less than two octaves. 

All that now remained was to plot the results on the chart. But 
just how was this to be done? To this question I had so far given 
almost no thought, feeling sure that some form of the co-ordinate 
system now everywhere used in statistical work could easily be adapted 
to the needs of the case. But confronting the problem directly, and 
with no record of previous attempts to guide me, I found myself at 
a loss. On reflection, however, it occurred to me that since the whole 
purpose of this study was to secure a plotted figure which should 
supplement and correct the imperfect and fleeting image of the sound 
formed in the mind, the plotted figure must be really comparable 
with the mental one — must have the same essential plan and structure. 
That is, the two must have the same system of co-ordinates. This 
brought me to the question, How does the mind image pitch? 

In listening to the flow of speech, it is probable that the mind 
does not ordinarily form any distinct image of the sensation of pitch. 
For the attention is then directed to the ensemble by which the mind 
recognizes words and phrases, and follows the general drift of thought 
rather than any one of the many separate elements which together 
make up the utterance. 3 Ordinarily the function of pitch in speech 
is a very subordinate one, being either incidental to emphasis, or 
suggestive of the syntactical or modal features of the utterance. So 
far is it from being an essential element, that it is entirely omitted 
in the written form of all languages except, of course, those in which 
voice-inflection is as truly an organic feature of words as are their 
vowels and consonants. 4 Within the field of speech, therefore, we 
shall look in vain for any clear answer to our question, How does 
the mind image pitch? 

If, however, we turn to music, we find that in it pitch is no longer 

s To this fact is due in large part the difficulty which European students 
experience in understanding and mastering the " tones" of Chinese speech. 
Their minds have never been trained to take note of the pitch of individual 
words, and therefore they never really hear it. 

* Chinese writing represents a word in its entirety by a single ideographic 
symbol. The "tone" is inherent in the word itself, just as are all the other 
phonetic elements which together make up its complex. It therefore needs 
no separate indication. So far as known to the writer, the only modern language 
which consistently marks voice-inflection in writing is the Siamese, which, 
though an offshoot of the Chinese stock, spells its words phonetically and 
indicates the "tone" of each, either by the choice of letters in which tone 
is inherent, or else by diacritical marks. The accents of ancient Greek, 
however, were doubtless also tonal inflections essential to the right utterance 
of the syllable, and were undoubtedly present in speech long before, it became 
necessary to invent marks to indicate their nature and position in the word. 



1916] 



Bradley: On Plotting the Inflections of the Voice 



199 



subordinate or incidental, but a matter of prime importance. There 
is no doubt that when the mind pauses to consider the notes of music, 
it does actually image their tonal relations — does translate them into 
figures of location or of movement in space. To discover the essential 
features of this imaging we shall not need to have recourse to the 
psychological laboratory. They are plainly indicated in the terms 
which the speech of widely different races commonly applies to musical 
tones. Degrees of pitch are indicated by such terms as "high" and 
"low." Direction of change, or movement in pitch, are indicated 
by such terms as "rising," "falling," and "level." And further, 
wherever these terms occur, they are invariably used in the same sense. 
That is, notes of great frequency of vibration are always "high," 
and those of small frequency are always "low," and never vice versa. 5 
The whole scheme of our musical notation is nothing but an elaborate 
development and enforcement of this same principle. Its "staff" 
is a veritable ladder on which the notes are visibly ranked according 
to pitch. 

It should be remarked, however, that this particular usage of speech 
is not the only one that has been current in the world, or that is now 
current. And it is probably not the earliest usage, but one that has 
gradually won its way over the others. For example : of the three 
Greek accents already referred to, one was called ofu? (sharp), and 
another was called ftapvs (heavy) — terms certainly of an order alto- 
gether different from our terms "high" and "low," and apparently 
unrelated to each other. The third, irepiairw^evo^ (twisted about), is 
probably of our spatial order, for it designates the circumflex tone, 
which first rises and then falls, and so is actually turned about upon 
itself. Thus it appears that at the period when the tonal features of 
Greek speech came to be matters of thought and reflection, three 
separate analogies were already in the field, and each furnished one 
of the names then given to them. But it is significant that later still, 
when it became necessary to mark these inflections in writing to save 
them from being lost, the three marks were all of one system, and that 

5 Since there seems to be nothing either in the physics of sound or in the 
nature of the mind to bring about this unanimity, it must be ascribed to some 
very early and widespread convention based, perhaps, on some external and 
incidental thing in musical art, such, for example, as the relative positions 
in which the various notes of some primitive musical instrument were produced 
or played. One can easily imagine that the particular instrument was the 
pipe, a thing of immense antiquity, and still in use throughout the greater 
part of the world. It is, in fact, nothing but a whistle with a tube long 
enough for finger-holes, and played in the flageolet position. The notes lowest 
in pitch are thus sounded from the openings which are lowest in actual position, 
and those higher in pitch, from openings higher up on the tube. 



200 University of California Publications in Am. Arch, and Ethn. [Vol. 12 

one is our own of spatial representation. For the marks are really 
nothing but tiny diagrams of the gestures by which one might instinct- 
ively illustrate the three movements in pitch : / rising, \ falling, 
^ circumflex. "Sharp," the equivalent of the Greek term o£u?, 
still survives as a technical term in modern music for a note slightly 
raised in pitch; but its counter-term "flat" seems to be a recent 
invention, the logical basis of which is not clear. 

We have turned from the field of speech to that of music because 
only in music have the phenomena of pitch received the full attention 
necessary to the formulation of a usage which clearly reveals the 
workings of the mind in dealing with this matter. The usage of music 
shows that the modern mind at least has learned to visualize pitch 
spatially, as position on a vertical scale, with notes of shorter vibration 
above, and notes of longer vibration below. 

But pitch is not the only thing to be provided for in our 
scheme. Inflection of the voice has also the element of movement 
and change, and these can take place only in time. The chart must 
provide also for this other dimension, time. Fortunately there is 
here no difficulty, for the mind habitually co-ordinates space and time, 
and readily translates either one of these into terms of the other. It 
images time as the track of a moving point — that is, as a line. Unless 
otherwise determined by outside circumstances, the movement seems 
generally figured as horizontal, and from left to right across the field. 6 

The results of this excursus into the realm of psychology may be 
summed up as follows. The essential elements of the mental image 
of an inflection of the voice are two : pitch and time. Pitch is figured 
as position attained at a given instant on a vertical scale. Time is 
figured as advance from point to point measured on a horizontal scale. 
The inflection itself is figured as a line which is the resultant of these 
two components. 

These principles determined the general scheme of the chart to 
be as follows : The series of numbers derived from measurements 
and representing the various levels of pitch, are the vertical elements 
of the chart, that is, its ordinates ; and numbers representing the time- 
intervals are the horizontal elements, that is, its abscissas. 

There still remained the problem of spacing in both these dimen- 

6 Both these features are doubtless due to convention — perhaps both to 
the same convention, namely to the direction taken by Indo-European writing. 
Both are abundantly attested by our modern cartographic treatment of all 
statistical matter involving the element of time. In antiquity we find the 
same idea reflected in the Greek accent-marks already alluded to. How 
Arabians and Chinese image time I am unable to say. 



1916] 



Bradley : On Plotting the Inflections of the Voice 



20 L 



sions. Following the common practice in the plotting of statistics, 
the spacing was made uniform throughout each of these dimensions, 
but not alike in both. Unit-spaces on the co-ordinate paper were 
assigned to the vertical series of measurement-numbers representing 
the various levels of pitch; 7 and a constant small interval, sufficient 
to give the requisite spread to the figure and to bring out its features, 
was chosen, after experiment, as the horizontal time-interval of advance 
between successive stations on the chart. 

This scheme was carried out as follows : Beginning at the left-hand 
margin, the first measurement was entered as a pencil-dot at the 
beginning of the line which bore its number. The second was next 
entered upon its own numbered line, but advanced toward the right 
by the interval determined upon. The other measurements followed 
in their order, each on its own numbered line and at the same constant 
interval to the right, till all the measurements of that particular record 
were plotted. A continuous curving line was then drawn through the 
series of plotted points, and the figure so completed represented 
visually the whole movement or inflection of the voice in uttering 
that syllable. 5 In like manner the four other " tones" of the series 
were plotted upon the same sheet. Finally the whole was brought 
into approximate relation with concert-pitch by finding on a piano 
the pitch at which I habitually sounded the more level stretch of the 
' 1 middle tone" — which was F. From this the positions of the other 
notes of the diatonic scale were computed by the help of the well- 
known ratios of the musical intervals. 9 and their places were marked 
upon the margin. So far as I can ascertain, this was the first attempt 
ever made to plot from measurements the inflections of the human 
voice. The chart was completed in November, 1908, and was exhibited 
at a public meeting of the Siam Societ}^ in Bangkok on February 2 
following. 

The experiment was more successful than I had dared to hope. 
The results were perfectly clear and convincing. The general scheme 
was evidently right. Careful study, however, revealed a certain 
distortion of vertical values which interfered with accurate comparison 
of one of these figures with another in a different portion of the field 
— a distortion in kind not unlike the horizontal distortion of Mercator's 

7 In this case the measurement-numbers ran from 18 at the top of the 
sheet to 64 at the bottom. Cf. plate 2 and p. 198 ante. 

s The figure so plotted is the rising- glide shown in plate 2, which is a 
reproduction of my original chart published in the Journal of the American 
Oriental Society, xxxi, pt. 3, p. 286. 1911. 

9 Cf. Century Dictionary s. v. Interval. 



202 University of California Publications in Am. Arch, and Ethn. [Vol. 12 

maps. The source of it was found to be the equal spacing of the 
vertical series of numbers representing the levels of pitch. While 
these numbers increase from above downward in arithmetical pro- 
gression, the musical intervals, as plotted on the chart, increase in 
geometrical progression, with the result that any given interval of 
the lower octave occupies a vertical space just twice as great as the 
same interval of the upper octave. An upward sweep of an octave 
from middle pitch would appear only half as long as a descending 
sweep of an octave from the same starting-point. This distortion is 
brought out unmistakably if one compares the rising glide in plate 2 
with the falling one. The rising glide covers fourteen semitones, while 
the falling one covers six and one-half. Yet on the chart the vertical 
reach of the former is only a trifle greater than that of the latter. 10 
The distortion would be very much greater if voices of entirely different 
range, such for example as the masculine and the feminine, were 
plotted together according to this scheme and brought into comparison. 
In such a case, indeed, effective comparison would be almost impossible. 

Now the ear knows nothing whatever of measurements such as we 
have been making; but beyond question it recognizes all octave cycles 
as equal. "Whether this is due to the recognition directly by the ear 
of cycles of recurrent unison, or whether it was first suggested by 
the fact that, in instruments like the pipe, the upper and the lower 
octaves are played from the same openings and over the very same 
length of tube, are questions which need not detain us here. But if 
the octaves are equal, then it follows inevitably that the semitones — 
if they be equal divisions of the octave — are all equal to each other. 
This equality, moreover, is enforced by the almost universal use of 
the tempered scale for musical instruments played either with keys 
or with frets. Thus our visual imagination and our thought too, unless 
sophisticated by physics, follow suit of the ear and make the semi- 
tones equal. 

The error being thus located, the first step toward rectifying it 
was obvious and easy, namely, to make the semitone-intervals equal 

io This element of vertical distortion, coupled with another of horizontal 
distortion to be noticed later, may also be clearly seen if one compares figure 1 
of plate 5, where both errors are uncorrected, with figure 2 of the same plate, 
where both are eliminated. The vertical element works as gravity does, 
progressively diminishing all upward movement as represented on the chart, 
making it fall short of its due height; and progressively increasing all down- 
ward motion, making it overshoot its mark. The other (the horizontal) 
distortion gives to ascending motion a greater spread than is its due, and 
to descending motion a spread proportionately less-. The two together make 
the plotted figure of the rising inflection both shorter and flatter than it 
should be, and that of the falling inflection both deeper and steeper. 



1916] 



Bradley: On Plotting the Inflections of the Voice 



203 



upon the chart. So the symbols of the twelve semitones took the places 
previously occupied by the measurement-numbers on the imit-lines 
of the paper. But the next step — to find new places for those ousted 
numbers — was not by any means so easy. Indeed, it was long before 
any clear lead appeared. After much vain groping it suddenly flashed 
upon me one day that each semitone of the octave has its distinct 
numerical value, namely, its ratio to the fundamental note of the 
scale. And this numerical value it brings with it to the new position 
in which it has been placed. These decimal ratios of the semitones 
therefore, equally spaced, form the determining series of the corrected 
chart, in the intervals of which the integers of the measurements must 
be interpolated, each in its proper place. I had found the clew, but 
was by no means out of the labyrinth. 

The ratios of the diatonic scale already mentioned would not answer 
here, for their intervals are not equal. I was where no books of refer- 
ence were accessible, and I am not at all sure that I should have found 
what I wanted, if I had had them. Thrown back thus upon my own 
resources, I reflected that the octave ratios form a series in geometrical 
progression — 1. 2, 4, 8, 16, and so on — with the constant ratio of 2. 
The semitone-ratios of the tempered scale, therefore, must also form 
a geometrical progression of twelve terms within each octave. Since 
2 is the constant ratio of the octave series, the constant ratio of the 
semitone series must be that quantity which multiplied into itself 
twelve times will make 2 — that is, the twelfth root of 2. Fortunately 
my desert island afforded an article of furniture not often found in 
such places — a table of logarithms. With its help I soon worked out 
the series of ratios shown on the left-hand margin of plate 4 and in 
table 1 below. For convenience in plotting, and to get rid of a decimal 
place. 10 rather than 1 was assumed as unity. The computation cov- 
ered two octaves — twenty-four semitones — with numerical values 
ranging from 10 to 40, providing compass enough for any ordinary 
speaking voice in experiments such as these. 

The earlier scheme, it will be recalled, was concrete and practical, 
based on a series of numbers derived from actual measurements. This 
new scheme was begun with an ideal series of ratios, and I proceeded 
to work it out as an ideal scheme to the end, leaving to a later stage 
the question of its adjustment to concrete cases. So dealing with it, 
the problem of interpolation referred to above became a problem of 
finding the places, within this ratio-series, of the natural numbers 
from 10 to 40. The ratios are mostly decimal, though 10, 20, and 40 



204 



University of California Publications in Am. Arch, and Ethn. [Vol. 12 



at the octave points are integers, and two others, at the fifth below in 
each octave, differ but infinitesimally from 15 and 30. Five numbers 
were thus located at the start, and the particular space within which 
each one of the other numbers must be located was plainly disclosed. 
Their exact positions, however, were not so easily determined. The 
method of proportional parts was first tried, and it furnished an 
approximation sufficiently close to serve the purpose immediately in 
view. Indeed, that was the method used in plotting the "tones" of 
Chinese speech. 11 

Here I should have stopped. But the "pagan curiosity" with 
which I am sometimes reproached drove me on. There must be a 
real solution to a mathematical series so wonderfully strict and sym- 
metrical; and I must find it. Nevertheless I groped long in darkness 
before light broke upon me at last one morning as I awoke out of 
sleep. If I were to plot the curve of those semitone ratios, the levels 
at which the curve cuts the vertical unit-lines would be the true 
location of the integral numbers. Without delay I set myself to work. 
The result is shown in plate 4. figure 1. where the vertical distances 
(ordinates) of the integer levels may be read directly from the milli- 
meter divisions of the paper. 

Even so I was not satisfied. The solution was perfect of its kind, 
but the kind was instrumental and mechanical — not of pure science. 
I marvel now at my infatuation with the problem, but still more at 
my stupidity. Long before this, in computing the semitone-ratios. I 
had used — without recognizing it or so formulating it — the equation 
y = a x , wherein a is 12 V 2. and x is in turn each of the numbers of 
the natural series from 1 to 24. But the equation is really one of 
two variables. All that I now needed to do was to turn the equation 
about and solve it for the values of x when, a remaining constant, y 
is in turn each number of the natural series from 10 to 40. This 
all the time being within my reach, and with the diagram fully drawn 
and under my eyes, it was weeks before I recognized in it the solution I 
was seeking. Thus at last my calculus, fifty years out of mind, came 
back to me and laid the uneasy demon that so long had plagued me. 

The distortion of figure, in so far as it arose from the unequal 
spacing of the semitone intervals, was now completely corrected by 
respacing unequally the numbered levels of pitch in such a way that 

11 Cf. plate 3. from a chart first published in Proceedings of the American 
Philological Association, xly, page xliv, with abstract of the paper read. 
The paper was subsequently published in full in the Journal of the Boyal Asiatic 
Society, North China Branch, August, 1915. 



1916] 



Bradley: On Plotting the Inflections of tlie Voice 



205 



their intervals diminished from above downward just fast enough 
to leave the semitone intervals equal throughout the chart. Still 
another element of distortion, however, lurked in the equal horizontal 
spacing which was adopted at the start. The spaces there ought to 
vary also, for they represent the time-intervals between successive 
points in the record, and these vary of course with the pitch. It was 
some time. I am ashamed to say. before it became clear that the very 
same measurement which I plotted vertically as pitch, gave me also, 
in its aspect as time, the measure of forward movement. The single 
measurement, that is. gives both co-ordinates of the plotted point — a 
most unusual and surprising thing. 

It must not be supposed, however, that the whole of the measure- 
ment-number must be taken as the increment of advance. To do so 
would be to flatten the figure almost beyond recognition. All that 
is necessary is that the increment in each case be proportional to the 
number representing pitch. Some constant fraction of that number 
— say one-half or one-third — will suffice to give the figure the necessary 
spread. 

Reviewing now the discussion so far. we see that the general scheme 
for plotting inflections of the voice involves two dimensions, each 
with a different system of spacing. In the scheme as originally worked 
out. there was an error of distortion in each of these two dimensions, 
due to the equal spacing which was tentatively adopted in each. In 
the readjustment of the scheme described above both errors have 
been eliminated by substituting for the equal spacing in each dimension 
a spacing graduated proportionally to the measurement-numbers — 
inversely proportional in the case of the vertical intervals; directly 
proportional in the case of the horizontal. Inflections so plotted are 
capable of strictest comparison in all their features both with each 
other and with the records. It is difficult, moreover, to see how any 
other systematic error can creep in. for there are but these two 
dimensions in which it could operate, and but the one door of measure- 
ment by which it could enter. 

The revised scheme, as has been noted, is not built upon actual 
measurements, as was the first one, but upon an ideal system of 
abstract numbers or ratios, on the one hand, and of positions deter- 
mined by these, on the other. It is, moreover, limited to two octaves, 
a compass which includes the extreme range of voice in ordinary 
speech. The special advantage of such a scheme is that, being ideal, 



206 University of California Publications in Am. Arch, and Etlin. [Vol. 12 

it is capable of being adapted without difficulty to any concrete case. 
The essential feature of the plot (that is, the spacing of the numbered 
levels of pitch) is arranged once for all, and is never to be changed. 
Adjustment has to do only with the numbers which are attached to 
these levels, and it may be accomplished in either of two ways: (a) 
the numbers of the scheme may be raised to meet the actual measure- 
ments by use of a suitable multiplier, or ( b ) the measurement-numbers 
may be reduced by division to the dimensions of the scheme. There 
is little to choose between the two methods, save that there is probably 
less chance of mistake or confusion if the plotted scheme of numbers 
be kept unchanged, and the particular voice or the particular meas- 
urements be reduced to the standard, just as all barometric readings, 
for purposes of comparison, are reduced to sea-level. The whole 
process may be made clear by means of the following example together 
with its illustration in figure 2 of plate 4. 

In table 3, column 2 (p. 207), are given two series of measurements 
made in the course of my experiments with the " tones" of Siamese 
speech. The two are taken almost at random from my notes, and 
represent respectively the rising and the falling inflection. The 
measurements are of groups of six waves throughout. The extreme 
measurements are 30 and 110 — a large compass of voice, falling only 
a little short of two octaves. The smallest number in our scheme is 
10. The measurements may therefore be reduced to standard by 
dividing them throughout by 3. The results of the reduction are 
tabulated in column 3, and these are the figures to be used in the 
plotting. 12 

In table 2, column 1, are given the numbers attached to the levels 
of pitch in our scheme ; and opposite these in column 2 are given the 
ordinates of those levels, that is, the vertical distance of each measured 
from the starting-point at level 10 at the top of the sheet. These 
ordinates are the results of the computation described above (p. 201). 

We turn now to the co-ordinate paper on which the inflections are 
to be plotted. Vertically it should have twenty-four unit spaces — one 
for each semitone of the two octaves. Horizontally, the eighteen unit 
spaces usually found in the millimeter sheet will be ample for all needs. 

Beginning at the upper right-hand corner, we number each unit- 
line along the margin from 0 at the top to 21 at the bottom. This 
marking has nothing to do with the final plot and is not absolutely 

12 In many cases it may be found simpler to perform the reduction by 
multiplying and pointing off one decimal place. Thus, if the extreme measure- 
ments had been 27 and 95, we might have multiplied by 4 and pointed off thus: 
10.8 and 38.0. 



1916] 



Bradley: On Plotting the Inflections of the Voice 



207 



necessary, but is only intended to facilitate the reading of the milli- 
meter distances in the next operation. It should be done lightly with 
a pencil, so that it may be easily erased when it has served its purpose. 
It therefore does not appear in plate 1. 

Next, at a little distance within the right-hand margin, Ave mark 
the top line 10, the level with which our scheme begins. Its distance 
of course is zero. From table 2 we take the second distance, 16.5, 
and find its place between the 16th and 17th millimeter lines directly 
below 10. where we mark it with a short horizontal pencil-line, and 
number it as level 11. We find in the table the third distance, 31.6 
(measured also from line 10), and with the help of the marginal 
numbering of the unit-lines, we enter it in its place as level 12 — and 
continue the operation with constantly diminishing spaces, until we 
reach the 40th level at the 21th line near the bottom. This completes 
the preparation of the chart. 





Table 1 


Table 2 




Table 3 




The Semitone 


The 


Levels of 




Measurements 






Ratios 




Pitch 




Series 1 






Xumerical 




Vertical 






Horizontal 


Xo. 


Value 


Xo. 


Distance 


Xo. 


Original 


Reduced 


Interval 


0 


10.00 


10 


00.0 mm. 


1 


56 


18.7 


9 mm. 


1 


10.60 


11 


16.5 


2 


55 


18.3 


9 


2 


11.23 


12 


31.6 


3 


56 


18.7 


9 


3 


11.89 


13 


45.5 


4 


55 


18.3 


9 


4 


12.60 


14 


58.3 


5 


54.5 


18 


9 


5 


13.35 


15 


70.3 


6 


53.5 


17.8 


9 


6 


14.14 


16 


81.5 


7 


51 


17 


9 


7 


14.98 


17 


92.0 


8 


50 


16.7 


8 


8 


15.87 


18 


101.8 


9 


48 


16 


8 


9 


16.81 


19 


111.1 


10 


46 


15.3 


8 


10 


17.81 


20 


120.0 


11 


43 


14.3 


7 


11 


18.87 


21 


128.5 


12 


40 


13.3 


7 


12 


20.00 


22 


136.5 


13 


37 


12.3 


6 


13 


21.20 


23 


144.2 


14 


36 


12 


6 


14 


22.46 


24 


151.6 


15 


35.5 


11.6 


6 


15 


23.78 


25 


158.7 


16 


35 


11.5 


6 


16 


25.20 


26 


165.5 


17 


33 


11 


6 


17 


26.70 


27 


172.1 


18 


30 


10 


5 


18 


28.28 


28 


178.3 










19 


29.96 


29 


184.3 




Series 2 




20 


31.74 


30 


190.3 


1 


50 


16.7 


8 mm. 


21 


33.60 


31 


196.0 


2 


52 


17.3 


9 


22 


35.62 


32 


201.5 


3 


54 


18 


9 


23 


37.74 


33 


206.9 


4 


56 


18.7 


9 


24 


40.00 


34 


212.0 


5 


57 


19 


10 






35 


217.0 


6 


58 


19.3 


10 






36 


221.8 


7 


61 


20.3 


10 






37 


226.5 


8 


66 


22 


11 






38 


231.1 


9 


74 


24.7 


12 






39 


235.6 


10 


83 


27.7 


14 






40 


240.0 


11 


93 


31 


16 










12 


110 


36.7 


18 



208 



University of California Publications in Am. Arcli. and Ethn. [Vol. 12 



We come now to the actual plotting. Referring to table 3 for the 
reduced measurements (in column 3) we take the first one. 18.7. and 
enter it with a pencil-dot slightly above level 19 traced across the 
chart. Taking the next number. 18.3. we note its place just below 
level 18; and finding in column 1 its horizontal interval. 9 (one-half 
of 18.3). we enter the second point at the level ascertained, and 9 
millimeter spaces to the right of the first. The third point is again 
on level 18.7, and 9 mm. to the right of point 2. This process is 
continued until the series ends with point 18 at level 10, 126 mm. 
from the left-hand edge. Through this series of points a smoothly 
curving line is carefully drawn, which constitutes the figure or 
pattern of movement executed by the voice in that particular utterance. 

The plotting of the second series of measurements is carried out 
in the same way, and on the same sheet. Lastly, concert-pitch is found 
from the record of a C-fork taken at the same time with the other 
records, which in this case determines the level of C as 17.6. that is. 
near the 10th unit-line from the top. From this datum the places of 
the other notes of the musical scale are easily determined by assigning 
one unit-space to each semitone. 

This study demonstrates the immense superiority, in point of 
delicacy, of instrumental analysis over the trained ear. In plate 3. 
tone 1. are shown five examples of the utterance of the same short 
syllable in succession. The pitch was intended to be a perfectly level 
tone. The serpentine oscillations which our analysis reveals entirely 
escaped the sense of hearing, as did also the uncertainty of attack 
and finish, and the hesitation in mid-movement exhibited in many 
examples of other tones given in the same chart. In figure 3 
of plate 5 may be seen the vagaries of a singer's voice in ren- 
dering C natural — a continual wandering away from pitch followed 
by attempted correction and return. The ear fails utterly to detect 
errors of this dimension, for the whole portion of the note here shown 
on the chart occupied but 1.08 of a second of time. The instrument 
reveals even minute variations in the rate of a tuning-fork due to 
infinitesimal variations in the drag on the prongs of the fork as the 
recording point sweeps the surface of the paper. 

Transmitted April 3, 1916. 



EXPLANATION OF PLATE 1 



Specimen records taken with the Kousselot apparatus, reduced to three- 
fourths of their original dimensions. 

Numbers 1 to 5 are records of the five " tones" of long vowels in Siamese 
speech, namely, 1, Eising; 2, Circumflex; 3, Middle; 4, Depressed; 5, Falling. 
No. 1 has been marked off into groups of waves for measurement. Number 6 
is the record of an electric tuning-fork making 100 vibrations per second. 

The general features of movement and pitch which characterize these five 
11 tones" are shown in plate 2; and a brief indication of the part they play 
in actual speech is given in the explanation of that plate. For an account 
of the way in which the records are made, see footnote 1, pp. 196-197. 

The extreme delicacy of which these records are capable is shown in the 
case of the electric fork, the rate of which would naturally be supposed to be 
absolutely uniform within the limits of a single record. But measurement 
shows that the rate varied during the fraction of a second of time occupied 
in the process. The first forty waves of the record together measure two one- 
hundredths of an inch more than the last forty. This infinitesimal variation 
is probably due to infinitesimal differences in the drag of the recording point 
as it swings from side to side on the surface of the paper. 



[210] 



EXPLANATION OF PLATE 2 



Chart of the five " tones" of long vowels in Siamese, illustrating the 
earlier scheme of plotting. 

So far as known to the writer, this is the first attempt ever made to 
plot from actual measurements the inflections of the voice. It was made 
in November, 1908, and was exhibited at a meeting of the Siam Society held 
in Bangkok on February 2, 1909. 

The figures here shown were plotted from records of the writer's voice 
as he pronounced the one syllable na with the five modes of voice-inflection 
distinguished by the Siamese in their utterance of long vowels. The one 
syllable so uttered becomes five different words, which to the natives do not 
seem to be homophones at all, but as clearly different as seem to us the 
words bate, beat, bite, boat, boot, which differ only in vowel quality. The 
meaning of the five Siamese words, differing only in tone, are as follows: 



Syllable Inflection Meaning 

na rising thick 

circumflex uncle or aunt 

middle rice-field 

depressed indeed 

falling face, front 



[212] 



EXPLANATION OF PLATE 3 
Chart of the ' ' tones ' ' of Pekingese. 

In this chart the vertical distortion noted in the earlier scheme was 
corrected by giving to the levels of pitch a graduated instead of a uniform 
spacing. It has a further interest in its revelation of surprising eccentricities 
or inaccuracies in the performance of the human voice. Tone 1, for example, 
is heard by the ear as a tone perfectly level in pitch. Its serpentine oscilla- 
tions completely escape notice by the ear, as do also the uncertainty of attack 
and the hesitation in execution noticeable in many other figures of the chart. 

Pekingese scholars claim four separate 11 tones" for their dialect. But 
the chart would seem to show that there are really but three. The general 
figure or pattern of "tone" 2 is identical with that of "tone" 3, and instru- 
mental analysis fails to discover within the range of examples available any 
constant difference of detail which the ear could detect as a basis of distinction. 
It may be that there is a difference in vowel-quantity which does not appear 
in the examples chosen. 



[214] 



EXPLANATION OF PLATE 4 



Figure 1. — The semitone-ratios and the levels of pitch. 

The semitone-ratios are a series of numbers which express the relative 
time of vibration at the pitch of each semitone of the octave, when the 
vibration-time at the pitch of C is 10. These ratios, computed for two octaves, 
are shown at the left-hand margin of the chart, each on its unit-line. The 
ratios, it will be noted, are nearly all decimal. The problem is to find the 
precise levels within this decimal series at which the integers 11, 12, 13, etc., 
are to stand. The problem was solved graphically as follows: Each ratio 
(less 10, because we begin at the margin with 10) was plotted on the chart 
as a horizontal line. Through the ends of these lines a curve was drawn. 
The points in which this curve cuts the vertical unit-lines will mark the true 
levels of the various integral numbers. The vertical distance (ordinates) 
from 0 at the top of the chart to each of these levels may be read directly 
from the co-ordinate paper. The ordinates actually entered on the chart are 
those derived from a subsequent computation, and are carried out to one 
decimal place. 

Figure 2. — Illustration of the perfected scheme for plotting inflections 
without distortion in either dimension, aa is the figure of a rising inflection, 
and bb the figure of a falling inflection so plotted. For the data used and 
for detail of the method see table 3 and the adjacent text, p. 207, ante. 



[216] 



UNIV. CALIF. P'J 



mm 




f4/4- - 



- — 1 —- ;- 



EXPLANATION OF PLATE 5 
Figures 1 and 2. — Direct comparison of the two schemes of plotting. 
Figure 1 is the rising inflection (aa) and the falling inflection (bb) as 
originally plotted in plate 2. Figure 2 shows these same inflections replotted 
according to the perfected scheme. Comparison shows that aa of figure 1 is 
shorter and flatter and shows a greater time-dimension than does the cor- 
rected aa of figure 2, while bb of figure 1 is deeper, steeper, and has less 
time-dimension than the corrected bb of figure 2. 

Figure 3 is a representation of the performance of a singer's voice in 
rendering the C natural of a tuning-fork. It illustrates the same vagaries, 
the same uncertainties and attempted corrections which were shown in the 
case of the speaking voice in plate 3. 



[218J 



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